We propose a timed broadcasting process calculus for wireless systems where time-consuming communications are exposed to collisions. The operational semantics of our calculus is given in terms of a labelled transition system. The calculus enjoys a number of desirable time properties such as (i) time determinism: the passage of time is deterministic; (ii) patience: devices will wait indefinitely until they can communicate; (iii) maximal progress: data transmissions cannot be delayed, they must occur as soon as a possibility for communication arises. We use our calculus to model and study MAC-layer protocols with a special emphasis on collisions and security. The main behavioural equality of our calculus is a timed variant of barbed congruence, a standard branching-time and contextually-defined program equivalence. As an efficient proof method for timed barbed congruence we define a labelled bisimilarity. We then apply our bisimulation proof-technique to prove a number of algebraic laws.

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We propose a simple timed broadcasting process calculus for modelling wireless network protocols. The operational semantics of our calculus is given in terms of a labelled transition semantics which is used to derive a standard (weak) bi-simulation theory. Based on our simulation theory, we reformulate Gorrieri and Martinelli's timed Generalized Non-Deducibility on Compositions (tGNDC) scheme, a well-known general framework for the definition of timed properties of security protocols. We use tGNDC to perform a semantic analysis of three well-known key management protocols for wireless sensor networks: µTESLA, LEAP+ and LiSP. As a main result, we provide a number of attacks to these protocols which, to our knowledge, have not yet appeared in the literature.